Quantum simulation of chemistry via quantum fast multipole method

• URL: http://arxiv.org/abs/2510.07380v1
• Date: Wed, 08 Oct 2025 18:00:01 GMT
• Title: Quantum simulation of chemistry via quantum fast multipole method
• Authors: Dominic W. Berry, Kianna Wan, Andrew D. Baczewski, Elliot C. Eklund, Arkin Tikku, Ryan Babbush,
• Abstract summary: We describe an approach for simulating quantum chemistry on quantum computers with significantly lower complexity than prior work.<n>The approach uses a real-space first-quantised representation of the molecular Hamiltonian which we propagate using high-order product formulae.
• Score: 0.15664499958794106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Here we describe an approach for simulating quantum chemistry on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian which we propagate using high-order product formulae. Essential for this low complexity is the use of a technique similar to the fast multipole method for computing the Coulomb operator with $\widetilde{\cal O}(\eta)$ complexity for a simulation with $\eta$ particles. We show how to modify this algorithm so that it can be implemented on a quantum computer. We ultimately demonstrate an approach with $t(\eta^{4/3}N^{1/3} + \eta^{1/3} N^{2/3} ) (\eta Nt/\epsilon)^{o(1)}$ gate complexity, where $N$ is the number of grid points, $\epsilon$ is target precision, and $t$ is the duration of time evolution. This is roughly a speedup by ${\cal O}(\eta)$ over most prior algorithms. We provide lower complexity than all prior work for $N<\eta^6$ (the regime of practical interest), with only first-quantised interaction-picture simulations providing better performance for $N>\eta^6$. As with the classical fast multipole method, large numbers $\eta\gtrsim 10^3$ would be needed to realise this advantage.

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